curve #4972

y² = x³ − x² − 28237020551288744x + 1826300679272509563635568

a-invariants: [0, -1, 0, -28237020551288744, 1826300679272509563635568]
c-invariants: [1355376986461859728, -1577923778759186344209972416]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 15418498435441900656
discriminant (Δ): 27471584899559170751417857654648065052271788032
Faltings height: 8.0647
naive height: 125.2518
primes of bad reduction: 2, 3, 11, 13, 31, 59, 67, 79, 197, 257, 4583
regulator: 136556.3628543674037801108373458491972862332880669753
submitted by: The Wren
submitted at: 2026-10-21 00:46:48 UTC
last updated: 2026-10-21 00:46:48 UTC

Witness: 7 independent points log in to add more points →

(-185162284, 840493743648)
(70440466, 432189155398)
(154504964, 1073242714320)
(2448815426, 120902783834118)
(-129092203/4, 13155030030051/8)
(1617132164/49, 330839218407984/343)
(182188416698/1849, 2035170994116546/79507)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-21 00:46:48 UTC · history